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Can A and can В are both right circular cylinders. The radiu

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Can A and can В are both right circular cylinders. The radiu [#permalink] New post 17 Mar 2011, 13:46
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64% (02:12) correct 36% (00:57) wrong based on 47 sessions
Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?

(A) $1
(B) $2
(C) $4
(D) $8
(E) $16
[Reveal] Spoiler: OA
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 17 Mar 2011, 14:09
banksy wrote:
2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?
(A) $1
(B) $2
(C) $4
(D) $8
(E) $16


Let x be the radius of b and 2h be the height of B. Therefore, radius of A = 2x and height = h

Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h

cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16

Ans E
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 19 Mar 2011, 00:57
B -> pi * r^2*h

A -> pi * 4r^2 * h/2 = 2 * pi * r^2 * h

So, Vol of 1/2 of can B = vol of 1/4 can A

So can A will take 4 * 4 = $16 for gasoline.
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 19 Mar 2011, 01:52
banksy wrote:
2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?
(A) $1
(B) $2
(C) $4
(D) $8
(E) $16


Let radius of B be r and A be 2r
vol of B=πr^2h
vol of a=4πr^2h (radius= (2r)) == twice the volume of B

To fill 1/2 of B it cost 4$
to fill B it cost 8 $
to fill 2b ie (a) it cost 16$
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 19 Mar 2011, 02:05
banksy wrote:
2. (KP) Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?
(A) $1
(B) $2
(C) $4
(D) $8
(E) $16


Volume of right circular cylinder = 2πr^2h
Let Radius of Can A= 4
Height of can A = 2
Volume of Can A = 2*π*r^2*h
= 2*π*4^2*2
= 64π

Radius of can B = 2
Height of can B = 4
Volume of Can B= 2*π*r^2*h
= 2*π*2^2*4
= 32π

1/2 of B= 32π/2=16π

thus cost required to fill can A = (4/16π)*64π= $16
Ans E.
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 22 Sep 2013, 19:34
sorry guys the answer is $ 8. lets consider the radius of can A to be 2x. radius of can B to be x. let the height of can A be y. Let the height of can B be 2y. Volume of a can A (pie 4x^2y) Volume of can B (pie 2 x^2 y). Since volume of can B is exactly half of can A. It costs $8 to fill can A completely.
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Re: 2. (KP) Can A and can В are both right circular cylinders. T [#permalink] New post 22 Sep 2013, 23:26
Expert's post
mohnish104 wrote:
sorry guys the answer is $ 8. lets consider the radius of can A to be 2x. radius of can B to be x. let the height of can A be y. Let the height of can B be 2y. Volume of a can A (pie 4x^2y) Volume of can B (pie 2 x^2 y). Since volume of can B is exactly half of can A. It costs $8 to fill can A completely.


Notice that we a re told that it costs $4.00 to fill half of can B. so the correct answer is E, not D.

Can A and can В are both right circular cylinders. The radius of can A is twice the radius of can B, while the height of can A is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can A with the same brand of gasoline?

(A) $1
(B) $2
(C) $4
(D) $8
(E) $16

Volume of B = \pi{r^2}h
Volume of A = \pi{(2r)^2}(\frac{h}{2})=2\pi{r^2}h.

Thus the volume of can A is twice the volume of cam B.

If it costs $4.00 to fill half of can B, then it costs 4*$4=$16 to completely fill can A.

Answer: E.
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Re: Can A and can В are both right circular cylinders. The radiu [#permalink] New post 23 Sep 2013, 04:25
Thank you Bunuel. I guess the answer has been wrongly pointed out in the Kaplan tests.
Re: Can A and can В are both right circular cylinders. The radiu   [#permalink] 23 Sep 2013, 04:25
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